Problem: $f(x)=x^3-6$ $h(x)=\sqrt[3]{2x-15}$ Write $f(h(x))$ as an expression in terms of $x$. $f(h(x))=$
Answer: Let's write $h(x)$ as the input to function $f$. $f({h(x)})=({h(x)})^3-6$ Since $h(x)=\sqrt[3]{2x-15}$, this becomes: $\begin{aligned} f({h(x)})&=({\sqrt[3]{2x-15}})^3-6\\ \\ &=2x-15-6\\ \\ &=2x-21\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $f(h(x))=2x-21$